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Mathematics: UG Titles

In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model.

The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists, and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process.

This exciting body of work, encompassing important advances in probability and combinatorics over the last 40 years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation. Analysis of the functional.


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  • Alexey Ustinov 7, 5 5 gold badges 61 61 silver badges 83 83 bronze badges. If there indeed is, Dan Romik's fantastic book devoted to this and more would be the place to begin. Link to author page.


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    • I will update the post after giving it a read, hopefully having an answer to both questions. But maybe I miss something. Dan Romik Dan Romik 1, 15 15 silver badges 27 27 bronze badges. Sign up or log in Sign up using Google.

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